Short-time-window Patlak imaging using a population-based arterial input function and optimized Bayesian penalized likelihood reconstruction: a feasibility study

Study design and patient selection

This retrospective study was approved by the ethics committee on epidemiological studies of our institution, which waived the requirement for informed consent. This study enrolled consecutive 30 patients who underwent dynamic 18F-FDG-PET/CT to assess the disease activity of cardiac sarcoidosis (CS) from April 2019 to January 2021. These patients underwent a combined 75 18F-FDG-PET/CT scans. Patients with incomplete dynamic scans were excluded.

In a previous study [11], the usefulness of Patlak Ki images derived from an individual patient-based IF for evaluating the risk of clinical events was examined in 21 patients with CS who underwent 30 18F-FDG-PET/CT scans, and patients were enrolled between April 2019 and January 2020. These 30 18F-FDG-PET/CT scans were included in the 75 18F-FDG-PET/CT scans, because analyses of the differences or relationships in Ki images between the individual patient-based IF with a long time window and the population-based IF with a short time window were not examined in these 30 18F-FDG-PET/CT scans in the previous study [11].

Two 18F-FDG-PET/CT scans were excluded because of incomplete dynamic 18F-FDG-PET/CT scans. Finally, 30 patients (22 women and 8 men; mean age, 62 ± 11 years; age range, 39 − 78 years) with 73 18F-FDG-PET/CT scans were enrolled. The number of scans was one, two, three, four, and five in 10, 4, 10, 5, and 1 patients, respectively.

Imaging protocols

All patients were instructed to fast for ≥ 18 h before PET/CT, which resulted in a mean plasma glucose level of 106 mg/dl (range, 56–167 mg/dl) immediately before the 18F-FDG intravenous injection.

All 18F-FDG PET/CT examinations were performed on a Discovery MI PET/CT (GE Healthcare, Milwaukee, WI, USA). First, low-dose CT covering the entire heart was performed (slice thickness, 3.75 mm; pitch, 1.375 mm; 120 keV; auto mA (40–100 mA depending on patient body mass); reconstructed matrix size, 512 × 512) with the transaxial and craniocaudal fields of view (FOVs) of 70 and 20 cm, respectively, which were used for attenuation correction of the PET images. Thereafter, 18F-FDG [230 ± 26 MBq (range, 162–286 MBq)] was injected, and dynamic list-mode PET data (single-bed) covering the aforementioned craniocaudal FOV were acquired with the following PET frames. The acquisition began at the time of injection, with scan times of 10 s/frame for the first 2 min, 3 min/frame for the next frame, and 5 min/frame thereafter for a total of 60 min. The motion corrections including body motion and respiratory motion were not performed for the dynamic PET data. The PET transaxial spatial resolution was 3.9 mm full-width half-maximum in-plane. The registration of CT and reconstructed dynamic PET image was verified using the Attenuation Correction Quality Control (ACQC) application (GE Healthcare) on the PET/CT scanner.

Calculation of Ki

To determine the 18F-FDG kinetic parameters within each lesion, a linear approximation of the mathematical representation of the standard two-compartmental model with irreversible trapping was used according to Patlak analysis [5].

From Ci (tk), the 18F-FDG activity concentration in the lesion (Bq mLtissue−1) at a given time tk after injection, the analytical solution of the two-compartment model is given as:

$$C_ \left( \right) = }\int\limits_^ }} \left( t \right)}t + V_}} C_}} \left( \right)}$$

where Cp(tk) represents the 18F-FDG activity concentration in blood plasma at time tk (Bq mLblood−1) and Vp is the total blood distribution volume (i.e., the unmetabolized fraction of 18F-FDG in blood and interstitial volume).

The compartmental transfer rates, namely K1 (from blood to cell), k2 (from cell to blood), and k3 (from 18F-FDG to 18F-FDG-6-phosphate), were used to calculate Ki, the net influx rate, as follows: Ki = (K1 × k3)/(k2 + k3). The transfer rate k4 from 18F-FDG-6-phosphate to 18F-FDG is negligible because Patlak analysis assumes unidirectional uptake of 18F-FDG (k4 = 0). The Ki unit is ml/g/min.

Generation of Ki images with the individual patient-based IF as the reference images

The individual patient IF was determined by blood time–activity curves derived from PET [image-derived input functions (IDIFs)] as described previously [11], and the following region of interest (ROI) was set to determine the IF by one radiologic technician. The investigator was aware of the study purpose but blinded to clinical information. A 15-mm-diameter spherical ROI was manually drawn in the center of the ascending aorta on the registered image to reduce contaminants such as atherosclerotic plaques or smooth muscles in the arterial wall. Patlak analysis was performed over the period from 10 to 60 min after injection during steady state. The data were reconstructed using time of flight (TOF) with the BPL reconstruction algorithm including point spread function (PSF) modeling, a beta value of 700, and transaxial FOV of 50 cm as the individual patient-based Ki image. The matrix size was 128 × 128, and the voxel size was 3.91 × 3.91 × 2.78 mm3. The Ki images generated using the individual patient-based IF (hereafter individual patient-based IF Ki images) were used as the reference images for evaluated Ki images generated using the population-based IF (population-based IF Ki images).

Generation of population-based IF Ki images

The normalized average of the arterial IF was used as the population-based IF. The population-based IF was generated from the individual IFs of the first 12 patients during the inclusion period acquired using the aforementioned protocol by the following method; the correlations between IDIF [\(\int\limits_^ }} \left( t \right)}t}\) (integral of plasma activity Cp from time 0 to 50)] and plasma activity of aorta at the uptake time of 50 min (Ao-50) were analyzed by the linear regression analysis among these 12 patients. Thereafter, the individual population-based IF was determined using the acquired regression equation (Y = 113.76 + 97.16x; r = 0.98, p < 0.001) (Additional file 1: Fig. S1).

To generate the population-based IF Ki images, Patlak analysis was performed over the period from 40 to 60 min after 18F-FDG injection with the following reconstruction method; The dynamic PET data from 40 to 60 min post-injection were reconstructed into 3 frames (6 min, 7 min and 7 min) using the same matrix and FOV used for individual patient-based IF Ki images. The images were reconstructed using TOF with the BPL algorithms including PSF modeling with three different penalization factors (beta values of 350, 700, and 1000). Thus, three population-based IF Ki images were created using these beta values for each study (Ki-350, Ki-700, and Ki-1000).

Image analysis

One nuclear medicine technician and one nuclear medicine radiologist who were aware of the study purpose but blinded to clinical information interpreted the Ki images independently. Four different Ki images including one individual patient-based and three population-based IF Ki images were read simultaneously for each study. The researchers assessed myocardial visual quality for each Ki image using a four-point scale as follows: 0, myocardium not visible; 1, poor lesion conspicuity, the degree of myocardial 18F-FDG uptake is above background but is difficult to distinguish from background noise; 2, moderate conspicuity, the degree of myocardial 18F-FDG uptake is above background and distinguishable from background noise; and 3, good conspicuity, the degree of myocardial 18F-FDG uptake is above background and distinguishable from noise and the lesion circumference is definable [17] (Fig. 1). Scores of 0 and 1–3 were assigned as negative and positive, respectively.

Fig. 1figure 1

Myocardial visual quality on Ki images using a 4-point scale: 0 (a, circle), myocardium not visible; 1 (b, circle), poor lesion conspicuity; 2 (c, circle), moderate conspicuity; and 3 (d, circle), good conspicuity. The visible focal spot in the circle of panel (a) indicates the nipple

For the images interpreted as positive by the two independent observers, the following quantitative parameters were obtained: . Each observer set the volumes of interest (VOIs) for the four Ki images for each study independently. They manually placed the VOIs on a suitable reference fused axial image and then defined the craniocaudal and mediolateral extent encompassing the entire positive myocardial lesion, excluding any avid extracardiac structures, to obtain Ki-max. They next set a 40% threshold of Ki-max to automatically delineate a VOI equal to or greater than the 40% threshold of Ki-max to calculate Ki-mean and Ki-volume, respectively. In the quantitative analysis of Ki images, the same method for VOI setting was applied for each Ki image. Workstations (Xeleris or Advantage Windows Workstation 4.5; GE Healthcare) automatically calculated Ki-max, Ki-mean, and Ki-volume.

Statistical analysis

The inter-observer agreement of the visual rating was evaluated using κ statistics analysis, and κ was interpreted as follows: less than 0.20, slight agreement; 0.21–0.40, fair agreement; 0.41–0.60, moderate agreement; 0.61–0.80, substantial agreement; and 0.81 or greater, almost perfect agreement [18]. Linear regression analysis was used to assess the relationship between two quantitative variables. The Wilcoxon rank sum test was used to assess the difference between two quantitative variables. The McNemar test was used to examine differences in the rating of visual scores among the four Ki images.

Data were presented as mean and standard deviation. p < 0.05 was considered indicative of statistical significance, and all p values were two-tailed. MedCalc Statistical Software (MedCalc Software Ltd., Acacialaan 22, 8400 Ostend, Belgium) was used for the statistical analyses.

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